A large number of ostomy bags for receiving bodily waste from colostomy or ileostomy patients have been proposed in the prior art, cf. for example EP 0 259 184 and EP 703 762. The problem of conveniently and hygienically disposing the used bag has been addressed by several prior art documents, cf. for example EP 703 762, which discloses an inner bag made sufficiently water-impermeable to prevent leakage into the outer bag during the period of use, though—because of the existence of the outer bag—the inner bag need not be made from such durable material. Accordingly, the inner bag is made from a material which is water-impermeable over a short period, but which gradually dissolves over a more extended time period, such as from a biodegradable material. The inner bag is said to be of a structure which is weakened upon immersion in a WC bowl such that it becomes limp and is less buoyant thereby enabling it to be flushed away easily. The inner bag is enclosed within an outer bag which is formed from a material which acts as a barrier to flatus gasses and which is provided with a flatus filter. The inner bag is permeable to flatus gasses, so that such gasses may diffuse through walls of the inner bag into the outer bag, from which the flatus gasses escape through the flatus filter.